How do I clean a razor?

I have a Schick Quattro (the pink one) women’s razor that just gets clogged with hair. I swear I’m not a hairy beast and this has never happened with other razors that I’ve used. I think the “safety wires” that are supposed to protect you from cutting yourself create this problem. I’ve tried running it under water, using a tack, and shaking it under water, but none of this gets the hair out. Thoughts?